Question

Determine all boundary points for the inequality (x−2)(x+4)≥0.

Answer 1

To determine the boundary points for the inequality (x−2)(x+4)≥0, we consider the sign of the expression (x-2)(x+4) for different values of x. The boundary points are -4, 2, and any point in between.

Step-by-step explanation:

To determine all boundary points for the inequality (x-2)(x+4)≥0, we need to find the values of x for which the inequality is true.

We can do this by considering the sign of the expression (x-2)(x+4).

• When x < -4, both factors are negative, so the expression is positive.
• When -4 < x < 2, the factor (x-2) is negative and (x+4) is positive, so the expression is negative.
• When x > 2, both factors are positive, so the expression is positive.

Therefore, the boundary points of the inequality are -4, 2, and any point in between.